These selecta contain 761 of the more than 2600 pages of I. J. Schoenberg's published articles. The selection made and the grouping in which the papers are presented here reflect most strongly Schoenberg's wishes. The first volume of these selecta is drawn from Schoenberg's remarkable work on Number Theory, Positive Definite Functions and Metric Geometry, Real and Complex Analysis, and on the Landau Problem. Schoenberg's fundamental papers on Total Pos­ itivity and Variation Diminution, on P6lya Frequency functions and sequences, and on Splines, especially Cardinal Splines, make up the second volume. In addition, various commentaries have been provided. Lettered references in these refer to items listed alphabetically at the end of each commentary. Numbered references refer to the list of Schoenberg's publications to be found in each volume. Those included in these selecta are starred. It has been an honor to have been entrusted with the editorial work for these selecta. I am grateful to the writers of the various commentaries for their illuminating contributions and to Richard Askey for solid advice. Carl de Boor v Table of Contents Volume 1 C. de Boor: Foreword ... v Table of Contents, Volume 2 ix xi Publications of I. J. Schoenberg . 1 I. J. Schoenberg: A brief account of my life and work Number theory . 13 [1] Uber die asymptotische Verteilung reeller Zahlen mod 1 [18] On asymptotic distributions of arithmetical functions . 43 59 [22] Regular simplices and quadratic forms 67 P. Erdos: Commentary ........ .